625.603 Discussion Assignment 5 - Python/R/MATLAB/Julia

discussion-05.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "# Objectives\n",
    "\n",
    "This report fully solves Question 11.3.16, while also verifying the information given in the question by recalculating them.\n",
    "The secondary objective is to show case several numerical computing languages.\n",
    "Four languages will be covered:\n",
    "\n",
    "* [Python](https://www.python.org/)\n",
    "    * Using [SciPy](https://www.scipy.org/) and [statsmodels](statsmodels.org)\n",
    "* [R](https://www.r-project.org/)\n",
    "* [MATLAB](https://www.mathworks.com/)\n",
    "    * Using the [Statistics and Machine Learning Toolbox](https://www.mathworks.com/help/stats/)\n",
    "* [Julia](https://julialang.org/)\n",
    "    * Using the [JuliaStats](https://juliastats.org/) packages and the [JuliaPlots](http://docs.juliaplots.org/latest/) packages\n",
    "    \n",
    "We will use each one with as much support as the language and related libraries for the question at hand."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "# Introduction\n",
    "\n",
    "There are many languages to use for [numerical computing](https://en.wikipedia.org/wiki/List_of_numerical-analysis_software), for various reasons. We selected languages that seem prominent in the applied sciences and in particular data science. \n",
    "\n",
    "There are times when you have a choice to the language, and there are others times where you have to add to an existing project with. By showcasing likely languages, hopefully the reader will find this useful in using any of the languages covered.\n",
    "\n",
    "This [article](https://www.linkedin.com/pulse/r-vs-python-matlab-octave-julia-who-winner-siva-prasad-katru) is a subjective comparision of all the languages used. It provides context for the strengths and weaknesses of each.\n",
    "\n",
    "We use [SoS](https://vatlab.github.io/sos-docs/) to create this document, this is expanded upon in the appendix. As much as possible, we link the related documentation to all the heavy lifting functions that are used in the analysis for each language."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "# Problem Statement of Question 11.3.16\n",
    "\n",
    "We are tasked with answering the following questions.\n",
    "\n",
    "> Regression techniques can be very useful in situations where one variable say, $y$, is difficult to measure but $x$ is not. Once such an $xy$-relationship has been \"calibrated\", based on a set of $(x_i, y_i)$’s, future values of $Y$ can be easily estimated using $\\hat{\\beta_{0}} + \\hat{\\beta_{1}}x$. Determining the volume of an irregularly shaped object, for example, is often difficult, but weighing that object is likely to be easy. The following table shows the weights (in kilograms) and the volumes (in cubic decimeters) of eighteen children be-tween the ages of five and eight.\n",
    ">\n",
    "> (a) Construct a $95\\%$ confidence interval for $E(Y|14.0)$.\n",
    ">\n",
    "> (b) Construct a $95\\%$ prediction interval for the volume of a child weighing $14.0$ kilograms.\n",
    "\n",
    "The table stated in the problem will be processed in the next section."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "# Preamble\n",
    "\n",
    "Since a goal of this report is to resolve the above question with multiple languages, we will convert the data into a csv file that will be read by each language.\n",
    "\n",
    "We do this my loading the table as a string block from the table in the text book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "kernel": "SoS"
   },
   "outputs": [],
   "source": [
    "raw_data = \"\"\"\n",
    "17.1\t16.7\t15.8\t15.2\n",
    "10.5\t10.4\t15.1\t14.8\n",
    "13.8\t13.5\t12.1\t11.9\n",
    "15.7\t15.7\t18.4\t18.3\n",
    "11.9\t11.6\t17.1\t16.7\n",
    "10.4\t10.2\t16.7\t16.6\n",
    "15      14.5\t16.5\t15.9\n",
    "16      15.8\t15.1\t15.1\n",
    "17.8\t17.6\t15.1\t14.5\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "The data is such that we have four columns alternating between $x$ and $y$ data. There is a [recipe](https://docs.python.org/3/library/itertools.html#itertools-recipes) from the official python docs for `grouper` function that we take insperation from when creating the csv. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "kernel": "SoS"
   },
   "outputs": [],
   "source": [
    "iterator = iter(raw_data.split())\n",
    "csv_data = [\n",
    "    [float(x), float(y)]\n",
    "    for x,y in zip(iterator,iterator)\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "We then write the data to a temporary file in csv format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "kernel": "SoS"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/tmp/tmpgezvkqep\n"
     ]
    }
   ],
   "source": [
    "import csv\n",
    "import tempfile\n",
    "\n",
    "tfile = tempfile.NamedTemporaryFile(mode=\"r+t\",delete=False)\n",
    "\n",
    "with tfile:\n",
    "    csv_writer = csv.writer(tfile, delimiter=\",\")\n",
    "    csv_writer.writerow([\"Weight\", \"Volume\"])\n",
    "    for row in csv_data:\n",
    "        csv_writer.writerow(row)\n",
    "\n",
    "csv_filepath = tfile.name\n",
    "        \n",
    "print(csv_filepath)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "If the past couple code cells seems nonsensical to you, you don't need to worry. There is sublte python magic at play. We will display the contents of the created csv file next. We use some [bash](https://www.gnu.org/software/bash/) display the contents of the csv file, note that the following shell is in a bash environment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "kernel": "Bash"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weight,Volume\n",
      "17.1,16.7\n",
      "15.8,15.2\n",
      "10.5,10.4\n",
      "15.1,14.8\n",
      "13.8,13.5\n",
      "12.1,11.9\n",
      "15.7,15.7\n",
      "18.4,18.3\n",
      "11.9,11.6\n",
      "17.1,16.7\n",
      "10.4,10.2\n",
      "16.7,16.6\n",
      "15.0,14.5\n",
      "16.5,15.9\n",
      "16.0,15.8\n",
      "15.1,15.1\n",
      "17.8,17.6\n",
      "15.1,14.5\n"
     ]
    }
   ],
   "source": [
    "%expand\n",
    "# This is a bash cell.\n",
    "cat \"{csv_filepath}\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "We also use a bit of [SoS magic `%expand`](https://vatlab.github.io/sos-docs/doc/user_guide/expand_capture_render.html#Expand-input-magic-expand) to grab the variable `csv_filepath` from python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "# Python\n",
    "\n",
    "## Language Summery\n",
    "\n",
    "Python is a general purpose open source programming language, used for many other purposes. According the self reported [2020 Stackoverflow survery](https://insights.stackoverflow.com/survey/2020#technology-programming-scripting-and-markup-languages-professional-developers) it is the fourth most used scripting language and also third most loved lanauge. With such a large community, finding online help should be quite easy. And with it's use in other fields, integrating analysis into an exsiting python project should not be too difficult.\n",
    "\n",
    "The author personally uses it semi-regularly for his day to day where he is employed, as well as several personal projects. Though he will use other languages, python is his most conformtable language. Hence the bias towards it. We wholeheartedly recommend learning python and the python related tools you need to be able to do your work. Being able to do computationally intensive analytical work, without asking for an expensive licence makes it easier for small-medium businesses hire you. Furthermore, it is quite liekly that you can integrate your work into an existing project with the many \"in-production\" python projects out there in the world.\n",
    "\n",
    "As much praise as the offers for python, it needs to be said that it is a general purpose language first before being a scientific language. If you struggle with programming, you may want to consider other languages to get you started. (But python is by far one of the easiest general purpose language to start learning)\n",
    "\n",
    "You can find a quick summery of the syntax at [Learn X in Y](https://learnxinyminutes.com/docs/python/). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Bash"
   },
   "source": [
    "## Precomputation\n",
    "\n",
    "So lets begin. In addition to the base language we will be using [SciPy ecosystem](https://www.scipy.org/) of libraries as well as [statsmodels](https://www.statsmodels.org/)(built on top of scipy) for high level statistics interactions.\n",
    "\n",
    "We first wish load all the relevent libraries we need"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "\n",
    "from statsmodels.formula.api import ols\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "We'll also turn off some warnings since some future function calls will complain since our data set size is small."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [],
   "source": [
    "import warnings; warnings.simplefilter('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "We first grab the file path from the SoS main environment using [SoS magic `%expand`](https://vatlab.github.io/sos-docs/doc/user_guide/expand_capture_render.html#Expand-input-magic-expand) like before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/tmp/tmpgezvkqep\n"
     ]
    }
   ],
   "source": [
    "%expand\n",
    "t_filepath = \"{tfile.name}\"\n",
    "print(t_filepath)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "We now wish to load the data from the csv file using [`read_csv`](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.read_csv.html) into a [`DataFrame`](https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [],
   "source": [
    "df = pd.read_csv(t_filepath)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "We'll display the information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Weight</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>17.1</td>\n",
       "      <td>16.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.8</td>\n",
       "      <td>15.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10.5</td>\n",
       "      <td>10.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>15.1</td>\n",
       "      <td>14.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>13.8</td>\n",
       "      <td>13.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>12.1</td>\n",
       "      <td>11.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>15.7</td>\n",
       "      <td>15.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>18.4</td>\n",
       "      <td>18.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>11.9</td>\n",
       "      <td>11.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>17.1</td>\n",
       "      <td>16.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>10.4</td>\n",
       "      <td>10.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>16.7</td>\n",
       "      <td>16.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>15.0</td>\n",
       "      <td>14.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>16.5</td>\n",
       "      <td>15.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>16.0</td>\n",
       "      <td>15.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>15.1</td>\n",
       "      <td>15.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>17.8</td>\n",
       "      <td>17.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>15.1</td>\n",
       "      <td>14.5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Weight  Volume\n",
       "0     17.1    16.7\n",
       "1     15.8    15.2\n",
       "2     10.5    10.4\n",
       "3     15.1    14.8\n",
       "4     13.8    13.5\n",
       "5     12.1    11.9\n",
       "6     15.7    15.7\n",
       "7     18.4    18.3\n",
       "8     11.9    11.6\n",
       "9     17.1    16.7\n",
       "10    10.4    10.2\n",
       "11    16.7    16.6\n",
       "12    15.0    14.5\n",
       "13    16.5    15.9\n",
       "14    16.0    15.8\n",
       "15    15.1    15.1\n",
       "16    17.8    17.6\n",
       "17    15.1    14.5"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "Well define our significane level."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [],
   "source": [
    "alpha = 0.05"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "We'll now compute the linear model using the [`ols`](https://www.statsmodels.org/devel/generated/statsmodels.regression.linear_model.OLS.html) function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [],
   "source": [
    "model = ols(\"Volume ~ Weight\", data=df).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "We'll display the model summery."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>Volume</td>      <th>  R-squared:         </th> <td>   0.993</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.993</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   2312.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Wed, 02 Dec 2020</td> <th>  Prob (F-statistic):</th> <td>9.81e-19</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>14:27:09</td>     <th>  Log-Likelihood:    </th> <td>  4.3323</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    18</td>      <th>  AIC:               </th> <td>  -4.665</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    16</td>      <th>  BIC:               </th> <td>  -2.884</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   -0.1040</td> <td>    0.312</td> <td>   -0.333</td> <td> 0.743</td> <td>   -0.765</td> <td>    0.557</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Weight</th>    <td>    0.9881</td> <td>    0.021</td> <td>   48.082</td> <td> 0.000</td> <td>    0.944</td> <td>    1.032</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.138</td> <th>  Durbin-Watson:     </th> <td>   1.599</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.566</td> <th>  Jarque-Bera (JB):  </th> <td>   0.853</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.216</td> <th>  Prob(JB):          </th> <td>   0.653</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.025</td> <th>  Cond. No.          </th> <td>    100.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                 Volume   R-squared:                       0.993\n",
       "Model:                            OLS   Adj. R-squared:                  0.993\n",
       "Method:                 Least Squares   F-statistic:                     2312.\n",
       "Date:                Wed, 02 Dec 2020   Prob (F-statistic):           9.81e-19\n",
       "Time:                        14:27:09   Log-Likelihood:                 4.3323\n",
       "No. Observations:                  18   AIC:                            -4.665\n",
       "Df Residuals:                      16   BIC:                            -2.884\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -0.1040      0.312     -0.333      0.743      -0.765       0.557\n",
       "Weight         0.9881      0.021     48.082      0.000       0.944       1.032\n",
       "==============================================================================\n",
       "Omnibus:                        1.138   Durbin-Watson:                   1.599\n",
       "Prob(Omnibus):                  0.566   Jarque-Bera (JB):                0.853\n",
       "Skew:                          -0.216   Prob(JB):                        0.653\n",
       "Kurtosis:                       2.025   Cond. No.                         100.\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "And we'll specifically access the least square coefficents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.10404608618970812"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.params.Intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9880519420637347"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.params.Weight"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "We'll now plot a visualization of the data, the linear model, and the confidence interval of the input data. Note that `pandas` and `statsmodels` hook into `matplotlib` for plotting, and have means of forwarding keyword argunments to the underlying `matplotlib` call."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from statsmodels.graphics.regressionplots import abline_plot\n",
    "\n",
    "sample_confdata = model.get_prediction(df).summary_frame(alpha)\n",
    "\n",
    "fig, ax = plt.subplots(dpi=150)\n",
    "\n",
    "df.plot.scatter(x='Weight', y='Volume', label=\"Data\", ax=ax)\n",
    "\n",
    "abline_plot(\n",
    "    model_results=model,\n",
    "    color=\"black\",\n",
    "    # matplotlib has some latex parsing.\n",
    "    label=f\"Least Square ($\\\\hat{{y}} = {model.params.Intercept:.2f} + {model.params.Weight:.2f}x$)\",\n",
    "    ax=ax,\n",
    ")\n",
    "ax.plot(\n",
    "    df.Weight, sample_confdata.mean_ci_upper,\n",
    "    color=\"green\", alpha=0.8, linewidth=1, linestyle=':',\n",
    "    label=f\"alpha={alpha:.2f} confidence interval\",\n",
    ")\n",
    "ax.plot(\n",
    "    df.Weight, sample_confdata.mean_ci_lower,\n",
    "    color=\"green\", alpha=0.8, linewidth=1, linestyle=':',\n",
    ")\n",
    "ax.plot(\n",
    "    df.Weight, sample_confdata.obs_ci_upper,\n",
    "    color=\"cyan\", alpha=0.8, linewidth=1, linestyle=':',\n",
    "    label=f\"alpha={alpha:.2f} prediction interval\",\n",
    ")\n",
    "ax.plot(\n",
    "    df.Weight, sample_confdata.obs_ci_lower,\n",
    "    color=\"cyan\", alpha=0.8, linewidth=1, linestyle=':',\n",
    ")\n",
    "ax.legend(loc=\"upper left\", prop={'size': 7})\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "As you can see from the plot, we see that the confidence interval is most narrow near the $(\\bar{x}, \\bar{y})$, and get's wider the further away you get. The prediction interval seems to have a constant distance away from the line of linear model. With that out of the way, answer the question given.\n",
    "\n",
    "The calculation for all the above confidence and prediction intervals are verified with the application of formulas in the appendix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "## Part A - Python\n",
    "\n",
    "We wish to construct an $95\\%$ confidence interval for $E(Y|14)$.\n",
    "\n",
    "We set the weight observation we wish to inspect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [],
   "source": [
    "x_in = 14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "From he model we [`get_prediction`](https://www.statsmodels.org/stable/generated/statsmodels.regression.linear_model.OLSResults.get_prediction.html) which outputs [prediction result object](https://www.statsmodels.org/stable/generated/statsmodels.regression.linear_model.PredictionResults.html). Note that we had to input a dataframe that had the `Weight` column in."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [],
   "source": [
    "prediction = model.get_prediction(\n",
    "    pd.DataFrame(data={\"Weight\":[x_in]})\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "With the prediction result, we can set the alpha level we wish to use with the [`summary_frame`](https://www.statsmodels.org/stable/_modules/statsmodels/regression/_prediction.html#PredictionResults.summary_frame)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [],
   "source": [
    "result = prediction.summary_frame(alpha)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "With that we can result object we can extract the info we need for the confidence interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence interval: (13.6188, 13.8386)\n"
     ]
    }
   ],
   "source": [
    "print(f\"Confidence interval: ({result.mean_ci_lower[0]:.4f}, {result.mean_ci_upper[0]:.4f})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "## Part B - Python\n",
    "\n",
    "We wish to construct an $95\\%$ prediction interval for a child weighing $14$ kg.\n",
    "\n",
    "Using the `result` we had calculated before, we can also extract the prediction interval since it is for the same observation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction interval: (13.2871, 14.1703)\n"
     ]
    }
   ],
   "source": [
    "print(f\"Prediction interval: ({result.obs_ci_lower[0]:.4f}, {result.obs_ci_upper[0]:.4f})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "We have shown what we have been asked to calculate. As we will see in future sections, these values will be varified with other independent implementations in other languages."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "# R\n",
    "\n",
    "R is a stats focused open source programming language. It sees heavy use in academic statistics, and other applied science areas. Based off [2020 Stackoverflow survery](https://insights.stackoverflow.com/survey/2020#technology-programming-scripting-and-markup-languages-professional-developers) it's the 17th most used scripting language, and 16th most loved language. It's community isn't as large as python, but it isn't small either. Although due to it's niche focus, there are only a handfull of active and supported libraries. A counter example to that is due to it's high useage in statistical academia, many cutting edge software will appear in R first (with varying level of compatibility).\n",
    "\n",
    "R is a great language to start learning computational analysis. It does it's best to get out of the way of and let you analyze data. It has been a heavy influence on all other statistical package implementations in other languages.\n",
    "\n",
    "With it being open source, and having a deciently sized community, you can (at worst) likely jerry rig something to insert your analysis into an exsiting project.\n",
    "\n",
    "You can find a quick summery of the syntax at [Learn X in Y](https://learnxinyminutes.com/docs/r/). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "## Precomputation\n",
    "\n",
    "We'll follow a similar song and dance as before. We'll load the data up and plot the data, linear model, and confidence intervals. Though we will only use the base R functionality.\n",
    "\n",
    "Something of note is that we use the base plotting functionality. There are two other well know plotting alternatives in R, [`ggplot2`](https://ggplot2.tidyverse.org/) and [`lattice`](https://www.statmethods.net/advgraphs/trellis.html).\n",
    "\n",
    "To be clear, all the code cells in this section is running in R.\n",
    "\n",
    "First we load the csv file path into the R environment using the [SoS magic `%expand`](https://vatlab.github.io/sos-docs/doc/user_guide/expand_capture_render.html#Expand-input-magic-expand)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "%expand\n",
    "csv_file = '{tfile.name}'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "We then load the data into a dataframe (using [`read.csv`](https://www.rdocumentation.org/packages/utils/versions/3.6.2/topics/read.table)), and display it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "df = read.csv(csv_file)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 18 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>Weight</th><th scope=col>Volume</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>17.1</td><td>16.7</td></tr>\n",
       "\t<tr><td>15.8</td><td>15.2</td></tr>\n",
       "\t<tr><td>10.5</td><td>10.4</td></tr>\n",
       "\t<tr><td>15.1</td><td>14.8</td></tr>\n",
       "\t<tr><td>13.8</td><td>13.5</td></tr>\n",
       "\t<tr><td>12.1</td><td>11.9</td></tr>\n",
       "\t<tr><td>15.7</td><td>15.7</td></tr>\n",
       "\t<tr><td>18.4</td><td>18.3</td></tr>\n",
       "\t<tr><td>11.9</td><td>11.6</td></tr>\n",
       "\t<tr><td>17.1</td><td>16.7</td></tr>\n",
       "\t<tr><td>10.4</td><td>10.2</td></tr>\n",
       "\t<tr><td>16.7</td><td>16.6</td></tr>\n",
       "\t<tr><td>15.0</td><td>14.5</td></tr>\n",
       "\t<tr><td>16.5</td><td>15.9</td></tr>\n",
       "\t<tr><td>16.0</td><td>15.8</td></tr>\n",
       "\t<tr><td>15.1</td><td>15.1</td></tr>\n",
       "\t<tr><td>17.8</td><td>17.6</td></tr>\n",
       "\t<tr><td>15.1</td><td>14.5</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 18 × 2\n",
       "\\begin{tabular}{ll}\n",
       " Weight & Volume\\\\\n",
       " <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t 17.1 & 16.7\\\\\n",
       "\t 15.8 & 15.2\\\\\n",
       "\t 10.5 & 10.4\\\\\n",
       "\t 15.1 & 14.8\\\\\n",
       "\t 13.8 & 13.5\\\\\n",
       "\t 12.1 & 11.9\\\\\n",
       "\t 15.7 & 15.7\\\\\n",
       "\t 18.4 & 18.3\\\\\n",
       "\t 11.9 & 11.6\\\\\n",
       "\t 17.1 & 16.7\\\\\n",
       "\t 10.4 & 10.2\\\\\n",
       "\t 16.7 & 16.6\\\\\n",
       "\t 15.0 & 14.5\\\\\n",
       "\t 16.5 & 15.9\\\\\n",
       "\t 16.0 & 15.8\\\\\n",
       "\t 15.1 & 15.1\\\\\n",
       "\t 17.8 & 17.6\\\\\n",
       "\t 15.1 & 14.5\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 18 × 2\n",
       "\n",
       "| Weight &lt;dbl&gt; | Volume &lt;dbl&gt; |\n",
       "|---|---|\n",
       "| 17.1 | 16.7 |\n",
       "| 15.8 | 15.2 |\n",
       "| 10.5 | 10.4 |\n",
       "| 15.1 | 14.8 |\n",
       "| 13.8 | 13.5 |\n",
       "| 12.1 | 11.9 |\n",
       "| 15.7 | 15.7 |\n",
       "| 18.4 | 18.3 |\n",
       "| 11.9 | 11.6 |\n",
       "| 17.1 | 16.7 |\n",
       "| 10.4 | 10.2 |\n",
       "| 16.7 | 16.6 |\n",
       "| 15.0 | 14.5 |\n",
       "| 16.5 | 15.9 |\n",
       "| 16.0 | 15.8 |\n",
       "| 15.1 | 15.1 |\n",
       "| 17.8 | 17.6 |\n",
       "| 15.1 | 14.5 |\n",
       "\n"
      ],
      "text/plain": [
       "   Weight Volume\n",
       "1  17.1   16.7  \n",
       "2  15.8   15.2  \n",
       "3  10.5   10.4  \n",
       "4  15.1   14.8  \n",
       "5  13.8   13.5  \n",
       "6  12.1   11.9  \n",
       "7  15.7   15.7  \n",
       "8  18.4   18.3  \n",
       "9  11.9   11.6  \n",
       "10 17.1   16.7  \n",
       "11 10.4   10.2  \n",
       "12 16.7   16.6  \n",
       "13 15.0   14.5  \n",
       "14 16.5   15.9  \n",
       "15 16.0   15.8  \n",
       "16 15.1   15.1  \n",
       "17 17.8   17.6  \n",
       "18 15.1   14.5  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "We'll create the linear model using the [`lm`](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/lm) function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "model = lm(Volume~Weight,data=df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "And display the model summery and the coefficents to the line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = Volume ~ Weight, data = df)\n",
       "\n",
       "Coefficients:\n",
       "(Intercept)       Weight  \n",
       "    -0.1040       0.9881  \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "coef = coefficients(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>(Intercept)</dt><dd>-0.104046086189709</dd><dt>Weight</dt><dd>0.988051942063734</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] -0.104046086189709\n",
       "\\item[Weight] 0.988051942063734\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   -0.104046086189709Weight\n",
       ":   0.988051942063734\n",
       "\n"
      ],
      "text/plain": [
       "(Intercept)      Weight \n",
       " -0.1040461   0.9880519 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "We'll define our alpha level."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "alpha = 0.06"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "Turn off some warnings before we make our plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "And create out plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
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NUtYlEIIeMY9zzPO9WRK3GlYAd07ty5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GxsbBwUGn07388stFg+fOnfv73/+empq6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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(warn=-1) # We turn off some warnings\n",
    "\n",
    "confidence_intervals = predict(model, interval=\"confidence\", level=1-alpha)\n",
    "prediction_intervals = predict(model, interval=\"prediction\", level=1-alpha)\n",
    "\n",
    "point_order = order(df$Weight)\n",
    "\n",
    "plot(df$Weight, df$Volume, col='blue')\n",
    "abline(model)\n",
    "lines(\n",
    "    df$Weight[point_order],\n",
    "    confidence_intervals[,\"lwr\"][point_order],\n",
    "    col='green'\n",
    ")\n",
    "lines(\n",
    "    df$Weight[point_order],\n",
    "    confidence_intervals[,\"upr\"][point_order],\n",
    "    col='green'\n",
    ")\n",
    "lines(\n",
    "    df$Weight[point_order],\n",
    "    prediction_intervals[,\"lwr\"][point_order],\n",
    "    col='cyan'\n",
    ")\n",
    "lines(\n",
    "    df$Weight[point_order],\n",
    "    prediction_intervals[,\"upr\"][point_order],\n",
    "    col='cyan'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "## Part A - R\n",
    "\n",
    "We will calcualte a $95\\%$ confidence interval for $E(Y|14)$.\n",
    "\n",
    "We set the weight observation we wish to inspect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "x_in = 14"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "We use the [`predict`](https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/predict) function in R."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "result_conf = predict(model, newdata = data.frame(Weight=c(x_in)), interval=\"confidence\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 1 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>fit</th><th scope=col>lwr</th><th scope=col>upr</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>13.72868</td><td>13.61877</td><td>13.83859</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 1 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "  & fit & lwr & upr\\\\\n",
       "\\hline\n",
       "\t1 & 13.72868 & 13.61877 & 13.83859\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 1 × 3 of type dbl\n",
       "\n",
       "| <!--/--> | fit | lwr | upr |\n",
       "|---|---|---|---|\n",
       "| 1 | 13.72868 | 13.61877 | 13.83859 |\n",
       "\n"
      ],
      "text/plain": [
       "  fit      lwr      upr     \n",
       "1 13.72868 13.61877 13.83859"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_conf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "'Confidence Interval: (13.6188, 13.8386)'"
      ],
      "text/latex": [
       "'Confidence Interval: (13.6188, 13.8386)'"
      ],
      "text/markdown": [
       "'Confidence Interval: (13.6188, 13.8386)'"
      ],
      "text/plain": [
       "[1] \"Confidence Interval: (13.6188, 13.8386)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sprintf(\n",
    "    \"Confidence Interval: (%.4f, %.4f)\",\n",
    "    result_conf[,\"lwr\"],\n",
    "    result_conf[,\"upr\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "## Part B - R\n",
    "\n",
    "We wish to construct an $95\\%$ prediction interval for a child weighing $14$ kg. Which amounts to doing same as above, but instand with a prediction interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [],
   "source": [
    "result_pred = predict(model, newdata = data.frame(Weight=c(x_in)), interval=\"prediction\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 1 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>fit</th><th scope=col>lwr</th><th scope=col>upr</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>13.72868</td><td>13.2871</td><td>14.17027</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 1 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "  & fit & lwr & upr\\\\\n",
       "\\hline\n",
       "\t1 & 13.72868 & 13.2871 & 14.17027\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 1 × 3 of type dbl\n",
       "\n",
       "| <!--/--> | fit | lwr | upr |\n",
       "|---|---|---|---|\n",
       "| 1 | 13.72868 | 13.2871 | 14.17027 |\n",
       "\n"
      ],
      "text/plain": [
       "  fit      lwr     upr     \n",
       "1 13.72868 13.2871 14.17027"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "kernel": "R"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "'Prediction Interval: (13.2871, 14.1703)'"
      ],
      "text/latex": [
       "'Prediction Interval: (13.2871, 14.1703)'"
      ],
      "text/markdown": [
       "'Prediction Interval: (13.2871, 14.1703)'"
      ],
      "text/plain": [
       "[1] \"Prediction Interval: (13.2871, 14.1703)\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sprintf(\n",
    "    \"Prediction Interval: (%.4f, %.4f)\",\n",
    "    result_pred[,\"lwr\"],\n",
    "    result_pred[,\"upr\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "Note how the intervals stated for Part A and Part B matches the python values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "# MATLAB\n",
    "\n",
    "MATLAB is is quite stable in the academic and engineering world, but you must pay for it. MATLAB is probably the earliest attempt at making programming more accessible to scientists. So it isn't suprising that it is still prevalent. It's has heavy emphasis on optimizing for [vectorized arithmatic (array programming)](https://en.wikipedia.org/wiki/Array_programming), which is indicated by it's name sake Matrix-Laboratory.\n",
    "\n",
    "Here is another [learn x in y](https://learnxinyminutes.com/docs/matlab/) summery.\n",
    "\n",
    "Something worth noting is that [octave](https://www.gnu.org/software/octave/index) attempts to be an open source replacement for MATLAB. They specifically focus on making matlab scripts function output of the box in octave. An issue may arise if you require a specilized matlab toolbox for your work that isn't replicated in octave."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "R"
   },
   "source": [
    "## Precomputation\n",
    "\n",
    "A helpful tip is if you have any setup before you need to run a script, like exporting paths for 3rd party libraries, you can use have a [setup.m](https://www.mathworks.com/help/matlab/ref/startup.html?searchHighlight=startup.m) file in the same directory as your matlab script and it's contents is executed before your script.\n",
    "\n",
    "We restrict our use the base MATLAB and the [Statistics and Machine Learning Toolbox](https://www.mathworks.com/help/stats/index.html?s_tid=CRUX_lftnav)\n",
    "\n",
    "As a reminder all the code cells in this section is running in MATLAB.\n",
    "\n",
    "Like usual we load the csv file path into the MATLAB environment using the [SoS magic `%expand`](https://vatlab.github.io/sos-docs/doc/user_guide/expand_capture_render.html#Expand-input-magic-expand)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "kernel": "MATLAB"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "csv_file =\n",
      "\n",
      "    '/tmp/tmpgezvkqep'\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%expand\n",
    "csv_file = '{tfile.name}'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "We set the MATLAB kernal connected to JupyterLab to create plots in the document. There are other jupyter-matlab [inline graphics](https://github.com/imatlab/imatlab/#inline-graphics) configurations that can be looked up."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "kernel": "MATLAB"
   },
   "outputs": [],
   "source": [
    "imatlab_export_fig('print-png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "We then use the [`readtable`](https://www.mathworks.com/help/matlab/import_export/read-spreadsheet-data-into-table.html) function to read the csv file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "kernel": "MATLAB"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "table =\n",
      "\n",
      "  18x2 table\n",
      "\n",
      "    Weight    Volume\n",
      "    ______    ______\n",
      "\n",
      "     17.1      16.7 \n",
      "     15.8      15.2 \n",
      "     10.5      10.4 \n",
      "     15.1      14.8 \n",
      "     13.8      13.5 \n",
      "     12.1      11.9 \n",
      "     15.7      15.7 \n",
      "     18.4      18.3 \n",
      "     11.9      11.6 \n",
      "     17.1      16.7 \n",
      "     10.4      10.2 \n",
      "     16.7      16.6 \n",
      "       15      14.5 \n",
      "     16.5      15.9 \n",
      "       16      15.8 \n",
      "     15.1      15.1 \n",
      "     17.8      17.6 \n",
      "     15.1      14.5 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "table = readtable(csv_file)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "We fit the data in the table to a linar model using [`fitlm`](https://www.mathworks.com/help/stats/fitlm.html) and it returns a [linear model](https://www.mathworks.com/help/stats/linearmodel.html).\n",
    "\n",
    "Note that MATLAB has fixed the $\\alpha$ level to $0.05$. The author could not find out how to set a custom level of significance. Since it's the once we ask, we can use it to compare our results, but if you need a different level of significance, it seems that you would have to implement the analysis yourself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "kernel": "MATLAB"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "model = \n",
      "\n",
      "\n",
      "Linear regression model:\n",
      "    Volume ~ 1 + Weight\n",
      "\n",
      "Estimated Coefficients:\n",
      "                   Estimate       SE        tStat        pValue  \n",
      "                   ________    ________    ________    __________\n",
      "\n",
      "    (Intercept)    -0.10405       0.312    -0.33348        0.7431\n",
      "    Weight          0.98805    0.020549      48.082    9.8103e-19\n",
      "\n",
      "\n",
      "Number of observations: 18, Error degrees of freedom: 16\n",
      "Root Mean Squared Error: 0.202\n",
      "R-squared: 0.993,  Adjusted R-Squared: 0.993\n",
      "F-statistic vs. constant model: 2.31e+03, p-value = 9.81e-19\n"
     ]
    }
   ],
   "source": [
    "model = fitlm(table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "MATLAB"
   },
   "source": [
    "We display the coefficients from the linear model. This hasn't come up before this, but python indexing starts at `0`, like many other general purpose languages. While all the other languages (R, MATLAB, Julia) all start their indexing at `1`, which is common for many scientific focused languages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "kernel": "MATLAB"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "a =\n",
      "\n",
      "   -0.1040\n",
      "\n",
      "\n",
      "b =\n",
      "\n",
      "    0.9881\n",
      "\n"
     ]
    }
   ],
   "source": [
    "a = model.Coefficients.Estimate(1)\n",
    "b = model.Coefficients.Estimate(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "MATLAB"
   },
   "source": [
    "Some neat trivia, MATLAB has powerful plotting and has even influenced [`matplotlib`](https://matplotlib.org/users/history.html?highlight=history), the defacto plotting library in python and heavily borrows syntax from MATLAB (you can even tell by it's name).\n",
    "\n",
    "We make our usual plot, but without the prediction bounds. Notice how MATLAB has done a lot of the heavy lifing for this plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "kernel": "MATLAB"
   },
   "outputs": [
    {
     "data": {
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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(model);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "MATLAB"
   },
   "source": [
    "One of the reasons we don't plot the prediction bounds is because we require the curve fitting toolbox for that. Which we chose not to include."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "MATLAB"
   },
   "source": [
    "## Part A - MATLAB\n",
    "\n",
    "We will calcualte a $95\\%$ confidence interval for $E(Y|14)$, as usual.\n",
    "\n",
    "We set the weight observation we wish to inspect. Note that [`;`](https://www.mathworks.com/help/matlab/matlab_prog/matlab-operators-and-special-characters.html) suppreses output at the end of a statement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "kernel": "MATLAB"
   },
   "outputs": [],
   "source": [
    "x_in = 14;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "MATLAB"
   },
   "source": [
    "We calculate the confidence interval using the [`predict`](https://www.mathworks.com/help/stats/linearmodel.predict.html) function. \n",
    "Note that with MATLAB, alpha is fixed to 0.05. If you want a different alpha, you must run through the calculation yourself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "kernel": "MATLAB"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "y_hat =\n",
      "\n",
      "   13.7287\n",
      "\n",
      "\n",
      "y_conf =\n",
      "\n",
      "   13.6188   13.8386\n",
      "\n"
     ]
    }
   ],
   "source": [
    "[y_hat, y_conf] = predict(model,x_in)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "kernel": "MATLAB"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Interval: (13.6188, 13.8386)\n"
     ]
    }
   ],
   "source": [
    "disp(sprintf(\"Confidence Interval: (%.4f, %.4f)\", y_conf(1), y_conf(2)));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "MATLAB"
   },
   "source": [
    "These values matches with the above calculations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "MATLAB"
   },
   "source": [
    "## Part B - MATLAB\n",
    "\n",
    "We wish to construct an $95\\%$ prediction interval for a child weighing $14$ kg. As we said prior, we require another toolbox prediction intervals. In it's place we will calculate the prediction interval by applying Theorem 11.3.8.\n",
    "\n",
    "Note that you can make statements be multi-line by adding\n",
    "[`...`](https://www.mathworks.com/help/matlab/matlab_prog/continue-long-statements-on-multiple-lines.html) at the end of the statement.\n",
    "\n",
    "Note that to claculate the t-score, we use the [`tinv`](https://www.mathworks.com/help/stats/tinv.html) function which calculates the inverse cumulative distribution function of the Student's t distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "kernel": "MATLAB"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "x_bar =\n",
      "\n",
      "   15.0056\n",
      "\n",
      "\n",
      "y_sd =\n",
      "\n",
      "    0.2017\n",
      "\n",
      "\n",
      "t_value =\n",
      "\n",
      "    2.1199\n",
      "\n",
      "\n",
      "w_predict =\n",
      "\n",
      "    0.4416\n",
      "\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.05;\n",
    "\n",
    "n = height(table);\n",
    "\n",
    "x_bar = mean(table.Weight)\n",
    "y_hat_sample = a + b*table.Weight;\n",
    "y_sd = sqrt( ...\n",
    "    sum((table.Volume - y_hat_sample).^2) ...\n",
    "    / (n-2) ...\n",
    ")\n",
    "\n",
    "t_value = tinv(1-alpha/2, n-2) %\n",
    "\n",
    "w_predict = t_value * y_sd * sqrt( ...\n",
    "    1 + 1/n + ...\n",
    "    (x_in - x_bar).^2 / sum((table.Weight-x_bar).^2) ...\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "kernel": "MATLAB"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction Interval: (13.2871, 14.1703)\n"
     ]
    }
   ],
   "source": [
    "disp(...\n",
    "    sprintf(\"Prediction Interval: (%.4f, %.4f)\", ...\n",
    "        y_hat-w_predict, ...\n",
    "        y_hat+w_predict));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "MATLAB"
   },
   "source": [
    "This acts as confirmation that appling the Theorem 11.3.8 gives us the same results as the previous libraries did for the prediction interval."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "# Julia\n",
    "\n",
    "The new language on this list, but one that is gaining a lot of traction. It is open source general purpose language, but it's community is heavily scientific. A specific boon for julia is it's runtime speed over python and R.\n",
    "\n",
    "In the [2020 Stackoverflow survery](https://insights.stackoverflow.com/survey/2020#technology-programming-scripting-and-markup-languages-professional-developers) Julia made the list as the 25th most scripting language, but made the 6th most loved language.\n",
    "\n",
    "This is the first time that the author is actually using julia-lang, and was included for exploratory reasons. With it being the newest language of the selected, it has the smallest community (but a passionate and active one).\n",
    "\n",
    "Another [learn x in y](https://learnxinyminutes.com/docs/julia/) page."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "MATLAB"
   },
   "source": [
    "## Precomputation\n",
    "\n",
    "We'll be using [JuliaStats](https://juliastats.org/) packages and [JuliaPlots](http://docs.juliaplots.org/latest/) library (with the [StatsPlots](https://github.com/JuliaPlots/StatsPlots.jl) extenson)\n",
    "\n",
    "All the code cells in this section is running in Julia.\n",
    "\n",
    "We again load the csv file path into the Julia environment using the [SoS magic `%expand`](https://vatlab.github.io/sos-docs/doc/user_guide/expand_capture_render.html#Expand-input-magic-expand)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"/tmp/tmpgezvkqep\""
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%expand\n",
    "csv_file = \"{tfile.name}\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "MATLAB"
   },
   "source": [
    "Note that [`StatsKit`](https://github.com/JuliaStats/StatsKit.jl) is an alias library that import several libraries at once for convience. [`StatsFuns`](https://github.com/JuliaStats/StatsFuns.jl) is used to access statistical distribution functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [],
   "source": [
    "using StatsFuns\n",
    "using StatsKit\n",
    "using StatsPlots\n",
    "using Printf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "source": [
    "Read in the csv file using the [`CSV.read`](https://dataframes.juliadata.org/v0.11.7/man/getting_started.html#Importing-and-Exporting-Data-(I/O)-1) function into a [dataframe](https://dataframes.juliadata.org/stable/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>Weight</th><th>Volume</th></tr><tr><th></th><th>Float64</th><th>Float64</th></tr></thead><tbody><p>18 rows × 2 columns</p><tr><th>1</th><td>17.1</td><td>16.7</td></tr><tr><th>2</th><td>15.8</td><td>15.2</td></tr><tr><th>3</th><td>10.5</td><td>10.4</td></tr><tr><th>4</th><td>15.1</td><td>14.8</td></tr><tr><th>5</th><td>13.8</td><td>13.5</td></tr><tr><th>6</th><td>12.1</td><td>11.9</td></tr><tr><th>7</th><td>15.7</td><td>15.7</td></tr><tr><th>8</th><td>18.4</td><td>18.3</td></tr><tr><th>9</th><td>11.9</td><td>11.6</td></tr><tr><th>10</th><td>17.1</td><td>16.7</td></tr><tr><th>11</th><td>10.4</td><td>10.2</td></tr><tr><th>12</th><td>16.7</td><td>16.6</td></tr><tr><th>13</th><td>15.0</td><td>14.5</td></tr><tr><th>14</th><td>16.5</td><td>15.9</td></tr><tr><th>15</th><td>16.0</td><td>15.8</td></tr><tr><th>16</th><td>15.1</td><td>15.1</td></tr><tr><th>17</th><td>17.8</td><td>17.6</td></tr><tr><th>18</th><td>15.1</td><td>14.5</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|cc}\n",
       "\t& Weight & Volume\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64\\\\\n",
       "\t\\hline\n",
       "\t1 & 17.1 & 16.7 \\\\\n",
       "\t2 & 15.8 & 15.2 \\\\\n",
       "\t3 & 10.5 & 10.4 \\\\\n",
       "\t4 & 15.1 & 14.8 \\\\\n",
       "\t5 & 13.8 & 13.5 \\\\\n",
       "\t6 & 12.1 & 11.9 \\\\\n",
       "\t7 & 15.7 & 15.7 \\\\\n",
       "\t8 & 18.4 & 18.3 \\\\\n",
       "\t9 & 11.9 & 11.6 \\\\\n",
       "\t10 & 17.1 & 16.7 \\\\\n",
       "\t11 & 10.4 & 10.2 \\\\\n",
       "\t12 & 16.7 & 16.6 \\\\\n",
       "\t13 & 15.0 & 14.5 \\\\\n",
       "\t14 & 16.5 & 15.9 \\\\\n",
       "\t15 & 16.0 & 15.8 \\\\\n",
       "\t16 & 15.1 & 15.1 \\\\\n",
       "\t17 & 17.8 & 17.6 \\\\\n",
       "\t18 & 15.1 & 14.5 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "18×2 DataFrame\n",
       "│ Row │ Weight  │ Volume  │\n",
       "│     │ \u001b[90mFloat64\u001b[39m │ \u001b[90mFloat64\u001b[39m │\n",
       "├─────┼─────────┼─────────┤\n",
       "│ 1   │ 17.1    │ 16.7    │\n",
       "│ 2   │ 15.8    │ 15.2    │\n",
       "│ 3   │ 10.5    │ 10.4    │\n",
       "│ 4   │ 15.1    │ 14.8    │\n",
       "│ 5   │ 13.8    │ 13.5    │\n",
       "│ 6   │ 12.1    │ 11.9    │\n",
       "│ 7   │ 15.7    │ 15.7    │\n",
       "│ 8   │ 18.4    │ 18.3    │\n",
       "│ 9   │ 11.9    │ 11.6    │\n",
       "│ 10  │ 17.1    │ 16.7    │\n",
       "│ 11  │ 10.4    │ 10.2    │\n",
       "│ 12  │ 16.7    │ 16.6    │\n",
       "│ 13  │ 15.0    │ 14.5    │\n",
       "│ 14  │ 16.5    │ 15.9    │\n",
       "│ 15  │ 16.0    │ 15.8    │\n",
       "│ 16  │ 15.1    │ 15.1    │\n",
       "│ 17  │ 17.8    │ 17.6    │\n",
       "│ 18  │ 15.1    │ 14.5    │"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = CSV.read(csv_file, DataFrame)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "source": [
    "We create a linear model using the [`lm`](https://juliastats.org/GLM.jl/stable/manual/#Methods-applied-to-fitted-models-1) function. We link an [example](https://juliastats.org/GLM.jl/stable/examples/#Linear-regression-1) from the documentation for reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StatsModels.TableRegressionModel{LinearModel{GLM.LmResp{Array{Float64,1}},GLM.DensePredChol{Float64,LinearAlgebra.Cholesky{Float64,Array{Float64,2}}}},Array{Float64,2}}\n",
       "\n",
       "Volume ~ 1 + Weight\n",
       "\n",
       "Coefficients:\n",
       "─────────────────────────────────────────────────────────────────────────\n",
       "                 Coef.  Std. Error      t  Pr(>|t|)  Lower 95%  Upper 95%\n",
       "─────────────────────────────────────────────────────────────────────────\n",
       "(Intercept)  -0.104046   0.311998   -0.33    0.7431  -0.765452    0.55736\n",
       "Weight        0.988052   0.0205492  48.08    <1e-18   0.94449     1.03161\n",
       "─────────────────────────────────────────────────────────────────────────"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = lm(@formula(Volume ~ Weight), df)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "source": [
    "We display the coefficents."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2-element Array{Float64,1}:\n",
       " -0.10404608618970543\n",
       "  0.9880519420637345 "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a, b = coef(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "source": [
    "We set our alpha level. Like MATLAB, output can be suppresed by ending the statement with a `;`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [],
   "source": [
    "alpha = 0.05;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "source": [
    "We now create our plot that we have created in the previous three languages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [
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clip-path=\"url(#clip430)\" d=\"M 0 0 M2046.76 1263.23 L2051.02 1263.23 L2051.02 1299.25 L2046.76 1299.25 L2046.76 1263.23 Z\" fill=\"#000000\" fill-rule=\"evenodd\" fill-opacity=\"1\" /><path clip-path=\"url(#clip430)\" d=\"M 0 0 M2070.74 1264.69 L2075.42 1264.69 L2075.42 1295.31 L2092.25 1295.31 L2092.25 1299.25 L2070.74 1299.25 L2070.74 1264.69 Z\" fill=\"#000000\" fill-rule=\"evenodd\" fill-opacity=\"1\" /><path clip-path=\"url(#clip430)\" d=\"M 0 0 M2105.93 1276.31 Q2102.5 1276.31 2100.51 1278.99 Q2098.52 1281.66 2098.52 1286.31 Q2098.52 1290.96 2100.49 1293.65 Q2102.48 1296.31 2105.93 1296.31 Q2109.33 1296.31 2111.32 1293.62 Q2113.31 1290.94 2113.31 1286.31 Q2113.31 1281.7 2111.32 1279.02 Q2109.33 1276.31 2105.93 1276.31 M2105.93 1272.7 Q2111.48 1272.7 2114.65 1276.31 Q2117.83 1279.92 2117.83 1286.31 Q2117.83 1292.67 2114.65 1296.31 Q2111.48 1299.92 2105.93 1299.92 Q2100.35 1299.92 2097.18 1296.31 Q2094.03 1292.67 2094.03 1286.31 Q2094.03 1279.92 2097.18 1276.31 Q2100.35 1272.7 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      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_conf = GLM.predict(\n",
    "    model,\n",
    "    df,\n",
    "    interval=:confidence,\n",
    "    level=1-alpha,\n",
    ");\n",
    "sample_pred = GLM.predict(\n",
    "    model,\n",
    "    df,\n",
    "    interval=:prediction,\n",
    "    level=1-alpha,\n",
    ");\n",
    "\n",
    "@df df scatter(:Weight, :Volume, label=\"Data\", color=\"blue\")\n",
    "@df df plot!(\n",
    "    (x) -> a+x*b,\n",
    "    min(:Weight...),\n",
    "    max(:Weight...),\n",
    "    label=\"Least Squares\",\n",
    "    color=\"black\",\n",
    "    legend=:bottomright,\n",
    ")\n",
    "plot!(\n",
    "    df.Weight,\n",
    "    sample_conf.upper,\n",
    "    label=\"Confidence Interval Upper\",\n",
    "    color=\"green\",\n",
    "    linestyle=:dot,\n",
    ")\n",
    "plot!(\n",
    "    df.Weight,\n",
    "    sample_conf.lower,\n",
    "    label=\"Confidence Interval Lower\",\n",
    "    color=\"green\",\n",
    "    linestyle=:dot,\n",
    ")\n",
    "plot!(\n",
    "    df.Weight,\n",
    "    sample_pred.upper,\n",
    "    label=\"Prediction Interval Upper\",\n",
    "    color=\"cyan\",\n",
    "    linestyle=:dot,\n",
    ")\n",
    "plot!(\n",
    "    df.Weight,\n",
    "    sample_pred.lower,\n",
    "    label=\"Prediction Interval Lower\",\n",
    "    color=\"cyan\",\n",
    "    linestyle=:dot,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "source": [
    "## Part A - Julia\n",
    "\n",
    "We will calcualte a $95\\%$ confidence interval for $E(Y|14)$, as usual."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [],
   "source": [
    "x_in = 14;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "source": [
    "Since multiple modules export `predict`, we specify which function we want to use by specifying the module by calling `GLM.predict`.\n",
    "\n",
    "I had a hard time finding the documentation for the predict funcion, found a [doc string](https://github.com/JuliaStats/GLM.jl/blob/29a0e1c574a51d8574a79872b6c250364164a420/src/lm.jl#L204) in the source code explaning all the optional parameters.\n",
    "\n",
    "We'll now use `GLM.predcit` to calculate the confidence interval requested."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>prediction</th><th>lower</th><th>upper</th></tr><tr><th></th><th>Float64?</th><th>Float64?</th><th>Float64?</th></tr></thead><tbody><p>1 rows × 3 columns</p><tr><th>1</th><td>13.7287</td><td>13.6188</td><td>13.8386</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& prediction & lower & upper\\\\\n",
       "\t\\hline\n",
       "\t& Float64? & Float64? & Float64?\\\\\n",
       "\t\\hline\n",
       "\t1 & 13.7287 & 13.6188 & 13.8386 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "1×3 DataFrame\n",
       "│ Row │ prediction │ lower    │ upper    │\n",
       "│     │ \u001b[90mFloat64?\u001b[39m   │ \u001b[90mFloat64?\u001b[39m │ \u001b[90mFloat64?\u001b[39m │\n",
       "├─────┼────────────┼──────────┼──────────┤\n",
       "│ 1   │ 13.7287    │ 13.6188  │ 13.8386  │"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_conf = GLM.predict(\n",
    "    model,\n",
    "    DataFrame(Weight=[x_in]),\n",
    "    interval=:confidence,\n",
    "    level=1-alpha,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Interval: (13.6188, 13.8386)"
     ]
    }
   ],
   "source": [
    "@printf(\"Confidence Interval: (%.4f, %.4f)\",\n",
    "       res_conf.lower[1],\n",
    "       res_conf.upper[1],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "source": [
    "## Part B - Julia\n",
    "\n",
    "We wish to construct an $95\\%$ prediction interval for a child weighing $14$ kg. Which repeats the above steps but with a prediction interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><thead><tr><th></th><th>prediction</th><th>lower</th><th>upper</th></tr><tr><th></th><th>Float64?</th><th>Float64?</th><th>Float64?</th></tr></thead><tbody><p>1 rows × 3 columns</p><tr><th>1</th><td>13.7287</td><td>13.2871</td><td>14.1703</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& prediction & lower & upper\\\\\n",
       "\t\\hline\n",
       "\t& Float64? & Float64? & Float64?\\\\\n",
       "\t\\hline\n",
       "\t1 & 13.7287 & 13.2871 & 14.1703 \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "1×3 DataFrame\n",
       "│ Row │ prediction │ lower    │ upper    │\n",
       "│     │ \u001b[90mFloat64?\u001b[39m   │ \u001b[90mFloat64?\u001b[39m │ \u001b[90mFloat64?\u001b[39m │\n",
       "├─────┼────────────┼──────────┼──────────┤\n",
       "│ 1   │ 13.7287    │ 13.2871  │ 14.1703  │"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res_pred = GLM.predict(\n",
    "    model,\n",
    "    DataFrame(Weight=[x_in]),\n",
    "    interval=:prediction,\n",
    "    level=1-alpha,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "kernel": "Julia 1.0.5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Interval: (13.2871, 14.1703)"
     ]
    }
   ],
   "source": [
    "@printf(\"Confidence Interval: (%.4f, %.4f)\",\n",
    "       res_pred.lower[1],\n",
    "       res_pred.upper[1],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "# Conclusion\n",
    "\n",
    "In this report we solve Question 11.3.6 computationally using four different languages (Python, R, MATLAB, Julia) and the full suport each language provides for statisticall analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "# Appendix\n",
    "\n",
    "## Tools\n",
    "\n",
    "This document was created using [SoS (Script of Script)](https://vatlab.github.io/sos-docs/), which is a extension to [JupyterLab](https://jupyterlab.readthedocs.io/en/latest/). SoS allows the use of multiple languages to be used in a script form, or in a notbook document. It's a bit involved to get setup (each language needs to be configured), but with some command line/terminal configuration it is farily worth it.\n",
    "\n",
    "### Warning for Matlab\n",
    "\n",
    "Matlab is by far the most difficult language to configure to use python and thus with JupyterLab (and thus again by SoS). Pay very close attention to the instructions in [imatlab](https://github.com/imatlab/imatlab), and specifically the section on [inline graphics](https://github.com/imatlab/imatlab#inline-graphics).\n",
    "\n",
    "\n",
    "## Languages Not Covered\n",
    "\n",
    "### Ruby\n",
    "\n",
    "Ruby was intended to be convered, but was cut for time. A future version of this document may include this.\n",
    "\n",
    "According to the [2020 Stackoverflow survery](https://insights.stackoverflow.com/survey/2020#technology-programming-scripting-and-markup-languages-professional-developers) it is the 14th most used scripting language\n",
    "and 19th most loved language. So a still relevent to pay attention to. It is another general purpose open source language that is used for many applications and with a solid academic community. \n",
    "\n",
    "Here is a [learn x in y](https://learnxinyminutes.com/docs/ruby/) summery for ruby."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "## Solution with Minimal Library Assistance\n",
    "\n",
    "The purpose of this section is to calculate the values stated in this report though only using vectorized calculations. We will use python and libraries for vectorized arthmatic so that the code easily reflects the mathematics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import scipy.stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "SoS"
   },
   "source": [
    "We compute the coefficents of the simple linear model according to Theorem 11.3.1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.10404608618986799\n",
      "0.9880519420637452\n"
     ]
    }
   ],
   "source": [
    "n = len(df)\n",
    "x_bar = df.Weight.mean()\n",
    "x_sum = df.Weight.sum()\n",
    "x_sq_sum = (df.Weight**2).sum()\n",
    "\n",
    "y_bar = df.Volume.mean()\n",
    "y_sum = df.Volume.sum()\n",
    "\n",
    "xy_sum = (df.Weight * df.Volume).sum()\n",
    "\n",
    "b = (\n",
    "    n * xy_sum - x_sum * y_sum\n",
    ") / (\n",
    "    n * x_sq_sum - x_sum**2\n",
    ")\n",
    "a = y_bar - b * x_bar\n",
    "\n",
    "print(a)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5987211554602254e-13"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs(a - model.params.Intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0547118733938987e-14"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs(b - model.params.Weight)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "Thus the coefficents are within 13 decimal places manually calculated compared to the output of statsmodels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2017485780531374\n"
     ]
    }
   ],
   "source": [
    "y_hat_sample = a + b*df.Weight\n",
    "y_sd = np.sqrt(\n",
    "    np.sum((y_hat_sample - df.Volume)**2)\n",
    "    /\n",
    "    (n-2)\n",
    ")\n",
    "print(y_sd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1199052992210112\n"
     ]
    }
   ],
   "source": [
    "t_value = sp.stats.t.ppf(1-alpha/2, n-2)\n",
    "print(t_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "We applyTheorem 11.3.7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [],
   "source": [
    "w_conf_sample = t_value * y_sd * np.sqrt(\n",
    "    1/n +\n",
    "    (df.Weight - x_bar)**2 / ((df.Weight-x_bar)**2).sum()\n",
    ")\n",
    "\n",
    "y_conf_upper = y_hat_sample + w_conf_sample\n",
    "y_conf_lower = y_hat_sample - w_conf_sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "We test if the calculations differ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all(\n",
    "    np.abs(y_conf_upper - sample_confdata.mean_ci_upper) < 1e-13\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all(\n",
    "    np.abs(y_conf_lower - sample_confdata.mean_ci_lower) < 1e-13\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "kernel": "Python3"
   },
   "source": [
    "So our calculations agree to at least 13 decimal places, which tells us that the `statsmodels` library computes agree with the formula from Theorem 11.3.7\n",
    "\n",
    "We do the same with te prediction interval and apply Theorem 11.3.8."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [],
   "source": [
    "w_pred_sample = t_value * y_sd * np.sqrt(\n",
    "    1 + 1/n +\n",
    "    (df.Weight - x_bar)**2 / ((df.Weight-x_bar)**2).sum()\n",
    ")\n",
    "\n",
    "y_pred_upper = y_hat_sample + w_pred_sample\n",
    "y_pred_lower = y_hat_sample - w_pred_sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
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    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 70,
     "metadata": {},
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   "source": [
    "np.all(\n",
    "    np.abs(y_pred_upper - sample_confdata.obs_ci_upper) < 1e-13\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "kernel": "Python3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "np.all(\n",
    "    np.abs(y_pred_lower - sample_confdata.obs_ci_lower) < 1e-13\n",
    ")"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "Similarly the prediction intervals are within 13 decimal places of the output of statsmodels. With all the calculations being verified for all the sample data (for both confidence interval and predictino interval), we can further conclude (but do not show) the calculations for requested observation."
   ]
  }
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